Missing question: "At what time is the velocity again zero?"
Solution:
the acceleration of the particle is
[tex]a_x = (10 -t ) ms^{-2}[/tex]
the velocity of the particle is the derivative of the acceleration:
[tex]v_x = (10 t - \frac{1}{2}t^2 + v_0) ms^{-1} [/tex]
where [tex]v_0 = 0 m/s[/tex] is the initial velocity, given by the problem.
So, to find when the particle's velocity is again zero, we should just put vx=0 and find t:
[tex]10 t - \frac{1}{2} t^2 = 0 [/tex]
which has two solutions:
t=0 (beginning of motion)
[tex]t=20 s[/tex]
and so, the particle velocity returns to zero after 20 seconds.
